Document Z4Rqp8Z0bDGk0q8qK5XJk3n50

560._________________ _________ CHAPTER 31________ / 1946 Cuide When two plane surfaces of infinite size are parallel to each other and their surfaces are at different temperatures, the exchange of heat between the two is proportional to the difference between the fourth powers of their absolute temperatures. -This is also true when one surface is completely surrounded by another surface; for example, if one sphere is placed within another sphere, the flow of heat between the outer surface of the smaller sphere and the inner surface of the larger sphere is proportional to the fourth power of the absolute temperatures of the two surfaces. In a panel-heated room, the heated panel may be considered to be completely en closed by the remaining surfaces, because all heat radiated by the heated panel is inter cepted by those surfaces. Consequently, the flow of heat from the heated ceiling to the ^ room, by radiation, is proportional to the difference between the fourth powers of the absojute temperature of the ceiling and the absolute mean radiant temperature of the remaining surfaces. The rate at which a surface emits heat varies with the temperature of the surface and with other characteristics of the surface. For ordinary heat flow calculations it is Fig. 9. Heat Delivered to Room by Radiation from Panel sufficiently accurate to assume that the materials which are commonly used in building construction emit heat at a rate of: (T \4 Btuh per square foot . where - T is the absolute temperature of the surface in Fahrenheit degrees. On, this basis the flow of heat from the ceiling to its surrounding surfaces is at the rate of:-.; '. ' ' 480 X 0.156 [(j^)4 - (l)4] Btub. In order that this rate may be equal to 24,582 Btuh, T must be 572 and the ceiling temperature about 112 F. * Instead of calculating this temperature it may be taken from Fig. 9, as follows: The ceiling must deliver heat to the room,- by radiation, at the rate of 24,582/480 or 51 Btuh per square foot. Find 51 on the left margin and move horizontally to the intersection with a 62 MRT line, and from the .point of intersection to the lower margin and read about 112.F. . With a-.ceiling temperature of 112 F, the MRT of the room will be 480 X 112 + 1,536 X 62; the sum divided by 2,016, or 74 F. - If an air temperature of 68 F and an MRT of 74 F should not produce satisfactory .conditions, the ceiling temi>erature can easily be changed as necessary,by.changing the. temperature of the circulating water. %` ' Calculations like the preceding may also be made with the aid of Table 2. The rate at which the ceiling must radiate heat exceeds by 51 Btuh per square foot the rate at Panel Heating and Radiant Heating, 561 Table 2. Total Heat Emission by Radiation3 Boor OB MbIm Radiant TemperATUBB F Deo 30 35 40 45 46 . 47 48 49 50 51 52 . 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 Radiation in Btu per (square foot) (hour) emitted to surroundings with a tempera ture of absolute aero by bodies at various temperatures and with emissivity factor e Boot OB Mean Radiant Temper- e 1.00 e 0.95 e 0.90 t 0.80 aturb F Deo . 99.7 103.9 108.0 112.5 113.3 114.3 115.2 116.0 116.9 117.9 118.8 119.8 120.6 121.7 122.6 123.5 124.4 125.3 126.3 127.1 128.2 129.1 130.1 131.0 132.1 133.0 134.0 135:0 136.0 94.7 98.7 102.8 106.9 107.7 108.6 109.5 110.3 111.0 112.0 112.9 113.8 114.6 115.5 116.4 117.4 118.2 119.0 119.9 120.7 121.8 122.6 123.5 124.4 125.5 126.4 127.3 128.3 129.3 89.8 93.6 97.2 10i.3 102.0 102.9 103.8 104.5 105.3 106.4 10619 107.8 108.6 109.4 110.3 111.3 112.0 112.8 113.8 . 114.4 115.3 116.2 117.1 117.9 118.8 119.7 120.5 121.5 122.3 79.7 ' 83.1 86.4 89.0 90.8 91.5 92.3 92.8 93.6 94.4 95.1 95.9 96.6 97.3 98.1 98.9 99.6 100.3 101.1 101.8 102.6 103.3 104.1 104.8 105.8 106.4 107.2 108.0 108.8 71 72 73 74 75 80 85 90 100 110 120 130 140 150 160 170 180 190 200 210 220 250 300 350 400 450 500 550 600 Radiation in Btu per (square foot)-(hour) emitted to surroundings with a temperature of absolute aero by bodies at various temperatures and with emissivity factor e e 1.00 137.0 137.9 138.9 140.2 141.6 147.2 152.9 158.5 170.3 182.3 195.6 210.9 224.1 238.0 252:1 271.6 289.1 307.7 `326.5 349.3 373.0 439.5 577.3 743.0 945.8 1181.0 1470.0 1798.0 2181.0 e 0.95 130.1 131.0 132.0 133.1 134.4 140.0 145.2 150.5 161.7 173.2 185.7 200.4 212.9 226.1 239.8 258.0 274.9 292.1 310.2 331.9 - 354.4 417.6 548.2 705.8 898.5 1121.0 1396.0 1708.0 2072.0 e 0.90 123.3 124.0 124.9 126.1 127.4 132.5 137.6 142.7 153.2 164.2 176.1 189.8 201.8 214.4 226.9 244.5 260.1 276.9 293.9 314.3 335.7 395.6 519.6 668.6 850.8 1063.0 1323.0 1619.0 1962.0 e 0.80 . 109.7 110.3 111.0 112.1 113.2 117.9 122.4 126.9 136.2 146.0 156.5 168.8 179.2 190.5 201.8 217.2 231.3 246.1 261.3 279.5 298.2 351.6 461.8 594.3 756.5 944.0 1176.0 1439.0 1745.0 `These factors are calculated from the formula / 0.173 x rT**>\ V 100,000.000 ) where tt -- total radiation. Btu per (sq ft) (hr) e -- emissivity. T = absolute temperature, Fahrenheit degrees. which the ceiling receives radiant heat from its surroundings. Assuming the emissivity of the walls, floor, and ceiling to be 90 per cent of that of a black body, the heat radiated to the ceiling, from the surfaces whose MRT is 62 F, is (Table 2) at the rate of 115.3 Btuh per square foot; the ceiling must therefore radiate heat at the rate of 115.3 plus 51, or'166.3; its temperature must be (Table 2) between 110 F and 120 F, and, by interpolation, 112 F, as calculated. 7-. Select the medium for heating the ceiling panel. The medium may be electricity, steam, air, or water,, but usually is air or water. If air is used it is generally heated in the basement, passed up through hollow inside walls or through ducts in those walls, allowed to flow between the ceiling and the floor above, and returned to the basement through hollow outside walls or through ducts in those walls. If the walls and floors are constructed of hollow tile, the cells in the tile.can be placed so that they will form continuous ducts, through which the warm air can flow up the inside-walls, then between the ceiling and-the floor, above, and down the outside walls. In this way the walls and ceiling become heating.panels. , If water is used as the medium, the pipes through which the water circulates--almost always under forced circulation--are placed in the floor, walls, or ceiling in such a manner that as much as possible of the heat emitted by the pipes will be delivered to the space to be heated. . _.